Almost 800 rescued in St. John the Baptist Parish after Hurricane Ida

The Karnofsky Tailor Shop, a historic national landmark in New Orleans, is one of the multiple buildings that collapsed when Ida walloped the city.

The brick two-story shop, a former tailor business in the Central Business District of the city, dates back to 1913 and is where Louis Armstrong worked before embarking on his legendary jazz career.

The family that owned the shop provided a second home for Armstrong and loaned him money to purchase his first cornet, according to the National Park Service.

-ABC News' Ginger Zee

Louisiana Gov. John Bel Edwards told MSNBC Monday that search and rescue efforts are ongoing and he expects Ida's death toll to "go up considerably throughout the day."

Helicopters are surveying damage because it will take “many days” to reach Louisiana's southern coastal areas by ground, he said.

Nearly all of southeast Louisiana is without power, the governor said. All eight major lines that feed electricity to the New Orleans area have failed.

-ABC News' Josh Hoyos

FEMA administrator Deanne Criswell called Ida "one of the most catastrophic hurricanes to make landfall" in the Gulf Coast region and said the storm left multiple collapsed buildings in its wake, particularly in the area of Baton Rouge.

"Some of the initial reports that we're hearing are some building collapses across the area, significant structural damage to many buildings," Creswell said Monday on "Good Morning America." "We're seeing some barges and some vessels that may have been broken loose and we're also experiencing over a million power outages right at the moment."

Criswell said emergency teams were heading out on search-and-rescue missions after receiving reports of people trapped in their homes by flooding.

"This is significant. There is major damage," Criswell said. "We've got a lot of resources in place to support the state."

Criswell added that "my biggest concern is still the fragility of our health care system."

"It has been stressed from COVID-19 and the occupancy has been full," said Criswell.

She said some hospitals in the hardest-hit areas of Louisiana were operating on backup generators.

Criswell said the good news is that it appears levees in southeast Louisiana, particularly those around New Orleans, held up through the storm.

"We knew there could be some in the southern parts of Louisiana that would overtop and those are areas that did have a mandatory evacuation order in place," Criswell said. "But we brought in search and rescue assets, power restoration teams, food and water to support the shelter operations."

The president of hard-hit Jefferson Parish, Louisiana, told ABC's "Good Morning America" Monday that all communication lines with Grand Isle were down.

Cynthia Lee Sheng said about 40 people are believed to have stayed on the barrier island, located about 100 miles south of New Orleans.

"We have lost contact with them since yesterday afternoon," Sheng said. "We have first responder teams out there planning their strategy for today, ready to go out."

Sheng also said there were concerns about Lafitte, Louisiana, saying officials had received reports of people trapped in their attics by high water.

"This is an area if you want to think of it like swampland, there's alligators out there," Sheng said.

She said rescue workers have not been able to reach the area due to darkness and downed power lines.

In addition to thousands in the area losing power, Sheng said the parish was losing pressure in its water system.

"We've had a lot of water main breaks," she said. "Our water system is losing pressure and so in order to be able to fight fires, that is a very critical element. So, we're trying to clear roads to do those water repairs."

Sheng added, "We're a broken community right now."